Hey there.
Nope. It does not cost FSP to level composing. It's a free aspect of the game. It is easy to get fragments. People sell items to help others who wish to gain Frags but everyone can hunt enemies to get frags. This really is not required.
~ Grim
Well each potion creation costs gold. So it is not "free" as you say.
Attaining any sort of significant potion level and you are required to pump out potions all day long, not useful ones.. but just ones to get XP as easily as possible .... costing more gold and frags.
.... AND there is a big cost to those that get really high levels , skipping the potion creation time, especially on higher XP potions.
Due to this cost, both in FSP and in fragment amounts, only a small portion of players actually try to level composing seriously. Since potions can be guild locked it makes the most sense to have guild members with high composing levels make the potions and other members to help in fragment farming that do not want to shoulder the FSP cost. (Look at any high level composer bio - they have notes to the guild about how much each potion cost in fragments).
If there was a general guild composing center that was based on the highest crafter in that guild it would be another story, but noone is going to break down frags to make a level 180 Conserve potion, when their guildie can make them a level 220 at the same cost.
I think you should reconsider. It is more than just "everyone can get frags, so everyone can make potions"